Correlation Minor Norms, Entanglement Detection and Discord

TL;DR

This paper introduces Correlation Minor Norms, a novel entanglement detection method based on quantum correlations, which generalizes existing criteria, is experimentally accessible, and relates to quantum discord and entanglement entropy.

Contribution

It develops Correlation Minor Norms for entanglement detection, extending the CCNR criterion, and links these norms to quantum discord and entanglement entropy.

Findings

Correlation Minor Norms can detect entanglement more effectively than CCNR.

The scheme allows for direct measurement of correlations in experiments.

Correlation Minor Norms relate to quantum discord and entanglement entropy.

Abstract

In this paper we develop an approach for detecting entanglement, which is based on measuring quantum correlations and constructing a correlation matrix. The correlation matrix is then used for defining a family of parameters, named Correlation Minor Norms, which allow one to detect entanglement. This approach generalizes the computable cross-norm or realignment (CCNR) criterion, and moreover requires measuring a state-independent set of operators. Furthermore, we illustrate a scheme which yields for each Correlation Minor Norm a separable state that maximizes it. The proposed entanglement detection scheme is believed to be advantageous in comparison to other methods because correlations have a simple, intuitive meaning and in addition they can be directly measured in experiment. Moreover, it is demonstrated to be stronger than the CCNR criterion. We also illustrate the relation between the Correlation Minor Norm and entanglement entropy for pure states. Finally, we discuss the relation between the Correlation Minor Norm and quantum discord. We demonstrate that the CMN may be used to define a new measure for quantum discord.